The Government not allowing SSM to me is what's unconstitutional.
You're absolutely within your constitutional right to oppose it. I'll never begrudge someone the fact they oppose something. I will definitely have issues though if they expect me to think their idiotic reasons for opposition that can't actually stand up to reality should be something I just "accept" as legitimate.
You are constitutionally allowed to be against Same Sex Marriage because Jooboo, the giant cuban man in the sky told you through smoke rings that you should be opposed to it. I've got no issue with that.
However, if you can't give me any constitutional argument why its not gender discrimination other than Jooboo says its bad and therefore it'd hurt you if it was allowed, I'm not going to think your position is smart, constitutional, or intelligent. And if you tried to tell me it was legitimate I'd laugh at it, show you why its not, and ridicule it if you continue to push an issue that is against the constitution. And god help you if you later try to proclaim the constitution as your basis for allowing something in the future.
However, the act of being opposed to SSM is not in and of itself unconstitutional and I don't have any issue with someone having that stance in a general sense.